Diffractive optical element

ABSTRACT

A diffractive optical element may include sub-wavelength period stack-and-gap structured layers providing transmissive phase delay at a wavelength. The sub-wavelength period stack-and-gap structured layers may include a set of thin anti-reflection layers that are index matched to an environment or a substrate over a range of fill factors of the sub-wavelength period.

RELATED APPLICATION(S)

This application claims priority under 35 U.S.C. § 119 to U.S.Provisional Application No. 62/559,982, filed on Sep. 18, 2017, thecontent of which is incorporated by reference herein in its entirety.

TECHNICAL FIELD

The present disclosure relates to diffractive optical elements. Moreparticularly, some aspects of the present disclosure relate to adiffractive optical element (DOE) that provides a particular phase delaybetween regions of the DOE.

BACKGROUND

A diffractive optical element (DOE) may be used for directing a beam.For example, a DOE, such as a diffractive lens, a spot arrayilluminator, a spot array generator, a beam splitter, a Fourier arraygenerator, and/or the like, may be used to split a beam, shape a beam,focus a beam, and/or the like. A DOE may be integrated into a multicastswitch, a wavelength selective switch, a gesture recognition system, amotion sensing system, and/or the like. A multi-level surface reliefprofile may be selected for a surface relief DOE. For example, atwo-level (sometimes termed “binary”) surface relief profile may beselected for the surface relief DOE. The two-level surface reliefprofile may be selected to approximate a continuous surface reliefprofile and to enable use of a photolithographic procedure and/or anetching procedure to manufacture the DOE. A period of the two-levelsurface relief profile may be sub-wavelength to approximate a continuoussurface relief profile. A thin stack may be employed to form thetwo-level surface relief profile.

SUMMARY

According to some possible implementations, a diffractive opticalelement may include sub-wavelength period stack-and-gap structuredlayers providing transmissive phase delay at a wavelength. Thesub-wavelength period stack-and-gap structured layers may include a setof thin anti-reflection layers that are index matched to an environmentor a substrate over a range of fill factors of the sub-wavelengthperiod.

According to some possible implementations, a diffractive opticalelement may include a stack of layers including a set of anti-reflectionlayers. The stack of layers may be transmissive for a wavelength. Awidth of the stack of layers may be divided into a set of periods. Awidth of each period, of the set of periods, may be shorter than thewavelength. A period, of the set of periods, may have a fill factordefining a width of a gap in the period. Fill factors of differentperiods may be different. A depth of the gap may extend through thestack of layers and through the set of anti-reflection layers. Eachperiod, of the set of periods, may provide phase delay, at thewavelength, associated with a corresponding fill factor. Over a range ofdifferent fill factors, the set of anti-reflection layers may be indexmatched to an environment in the gap or to a substrate.

According to some possible implementations, a diffractive opticalelement may include stack-and-gap structured layers including at leastone layer sandwiched between a first set of anti-reflection layers and asecond set of anti-reflection layers. The stack-and-gap structuredlayers may provide transmissive phase delay at a wavelength. Thestack-and-gap structured layers may have a period shorter than thewavelength. A material composition, a thickness, and a quantity oflayers of the first set of anti-reflection layers and a materialcomposition, a thickness, and a quantity of layers of the second set ofanti-reflection layers may be selected such that, at the wavelength, agreater than 85% transmission efficiency is achieved over a range offill factors of the period.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of an overview of an example implementationdescribed herein;

FIG. 2 is a diagram of characteristics relating to an exampleimplementation described herein;

FIGS. 3A-3G are diagrams of example implementations described herein;and

FIGS. 4A-4D are diagrams of characteristics relating to an exampleimplementation described herein.

DETAILED DESCRIPTION

The following detailed description of example implementations refers tothe accompanying drawings. The same reference numbers in differentdrawings may identify the same or similar elements.

A diffractive optical element (DOE) may be manufactured using aphotolithographic procedure and/or an etching procedure. For example, toapproximate a continuous surface relief profile, a multi-level surfacerelief profile may be selected for the DOE, and a surface of the DOE maybe etched or patterned to form the multi-level surface relief profile.The multi-level surface relief profile may be used to create a phasedelay for a beam passing through the DOE. However, a diffractiveefficiency associated with the multi-level surface relief profile may beless than a threshold that is necessary for utilization of the DOE in anoptical system, such as an optical communication system, a gesturerecognition system, a motion detection system, and/or the like.Moreover, a transmittance of the multi-level surface relief profile maybe less than a threshold that is necessary for utilization of the DOE inthe optical system.

Some implementations, described herein, may provide a sub-wavelengthperiod stack-and-gap structured DOE providing transmissive phase delayat a wavelength, thereby achieving polarization independence for aperiodic grating based DOE. For example, some implementations, describedherein, may provide a two-level (also termed “binary”) DOE with athreshold transmittance for a threshold range of fill factors for thestack-and-gap structure of the DOE. Moreover, the DOE may be associatedwith a threshold diffractive efficiency, thereby enabling use in opticalsystems such as wavelength selective switches, spot array generators,and/or the like. In this way, a DOE may be formed with, for example, asingle masking step and etching step, thereby improvingmanufacturability relative to multi-level fabrication techniques,variable dosage laser writing techniques, e-beam writing techniques,and/or the like. Furthermore, layers of the thin-film stack may beindex-matched to a substrate of the DOE and/or an exit media. In thisway, the thin stack improves transmittance relative to other techniquesfor manufacturing a DOE.

FIG. 1 is a diagram of an overview of an example implementation 100described herein. FIG. 1 shows an example of spot array generation usinga DOE and a converging lens as a spot array illuminator (sometimestermed a spot array generator).

As shown in FIG. 1, an incident plane wave 110, with a wavelength of λ₀,is directed toward a DOE 120. In some implementations, DOE 120 may be acarrier grating with a varying fill factor, as described herein. Forexample, DOE 120 may be associated with a set of carrier periods, andeach carrier period may include at least one stack and at least one gap.A size of the at least one stack and the at least one gap in eachcarrier period may correspond to a fill factor, and the fill factor maybe configured to control a phase delay between carrier periods.

In some implementations, DOE 120 may include, for example, alternatingsilicon (Si) thin layers and silicon dioxide (SiO₂) thin layers,alternating hydrogenated silicon (Si:H) thin layers and silicon dioxidethin layers, and/or the like that are employed to form the stacks andgaps of the carrier grating. In some implementations, a size of acarrier period may be configured based on the wavelength of λ₀. Forexample, DOE 120 may be configured to be a sub-wavelength carriergrating with carrier periods associated with a width of less than thewavelength of λ₀. In some implementations, layers of DOE 120 may beconfigured to provide an anti-reflection functionality. For example, DOE120 may include a single set of index-matched thin layers to provide theanti-reflection functionality, multiple sets of index-matched thin filmlayers to provide the anti-reflection functionality, and/or the like. Insome implementations, a thin layer may be a layer with a thickness ofless than a threshold as described herein, such as a thin film layerand/or the like. In some implementations, the anti-reflectionfunctionality may be provided for a threshold range of fill factors,described herein.

In some implementations, incident plane wave 110 may have a wavelengthin a range from approximately 700 nanometers (nm) to approximately 2000nm, approximately 1000 nm to approximately 1800 nm, approximately 1400nm to approximately 1600 nm, approximately 1500 nm to approximately 1600nm, approximately 800 nm to 1000 nm, approximately 600 nm to 1000 nm,approximately 850 nm to 950 nm, and/or the like. Additionally, oralternatively, incident plane wave 110 may be associated with a centerwavelength of approximately 1550 nm, which may be a wavelength at whichDOE 120 provides a threshold phase delay, an anti-reflectionfunctionality, and/or the like. In some implementations, a maximumtransmissive phase delay provided by DOE 120 (e.g., between differentcarrier periods of DOE 120) may be greater than or equal to π, 2π, 4π,and/or the like. Additional details regarding DOE 120 are describedherein.

As further shown in FIG. 1, DOE 120 diffracts incident plane wave 110,and directs wavefront 130 (e.g., diffracted orders of incident planewave 110) toward a converging lens 140. Converging lens 140 is separatedby a focal distance 150 from a focal plane 160. In some implementations,example implementation 100 may be used for a gesture recognition system,and focal plane 160 may be a target for gesture recognition.Additionally, or alternatively, focal plane 160 may be an object (e.g.,for a motion sensing system), a communications target (e.g., for anoptical communications system), and/or the like.

As further shown in FIG. 1, based on converging lens 140 altering anorientation of wavefront 130 to form wavefront 170, wavefront 170 isdirected toward focal plane 160 causing a multiple spot array pattern tobe formed at focal plane 160. In some implementations, DOE 120 may beused to create a one-dimensional spot array. In some implementations,DOE 120 may be used to create a two-dimensional spot array. In this way,a DOE may be used as a spot array illuminator to create a spot array atfocal plane 160 from incident plane wave 110, thereby enabling a gesturerecognition system, a motion sensing system, an optical communicationssystem, and/or the like.

As indicated above, FIG. 1 is provided merely as an example. Otherexamples are possible and may differ from what was described with regardto FIG. 1.

FIG. 2 is a set of diagrams 202-210 of characteristics relating to a setof DOEs. As shown in FIG. 2, and by diagrams 202-210, the set of DOEsmay be associated with different relief profiles for refractive lensesof the set of DOEs.

As further shown in FIG. 2, and by diagram 202, a first DOE may beassociated with a continuous phase relief profile for a refractiveoptical element (e.g., a lens). The first DOE may provide a continuousexperienced phase delay from 0 to a maximum phase delay across a surfaceof the first DOE. Although described herein as a 0 phase delay, the 0phase delay may be a minimum phase delay. In other words, the 0 phasedelay may be a 0 relative phase delay, and the maximum phase delay maybe a maximum relative phase delay (relative to the 0 phase delay). Asfurther shown by diagram 204, a second DOE may be associated with amodulus 2 π Fresnel zone continuous phase diffractive optic. The secondDOE may provide a periodic continuous phase delay from 0 to a maximumphase delay across a surface of the second DOE. For example, the secondDOE may include a first region with an experienced phase delay of 0 tothe maximum phase delay, a second region with an experienced phase delayof 0 to the maximum phase delay, and a third region with an experiencedphase delay of 0 to the maximum phase delay.

As further shown in FIG. 2, and by diagram 206, a third DOE may beassociated with a periodic n-level (e.g., two or more level) reliefprofile. For example, the third DOE may include a plurality of discretelevels, each associated with a different experienced phase delay from 0to a maximum phase delay. In this case, the third DOE includes a firstregion with a first level with a first phase delay of 0, a second levelwith a second phase delay between 0 and a maximum phase delay, and athird level with a third phase delay of the maximum phase delay; asecond region with the first level, second level, and third level; and athird region with the first level, second level, and third level. Asfurther shown by diagram 208, a fourth DOE may be associated with aperiodic graded index phased array liquid crystal on substrate (LCOS)optical element. For example, the fourth DOE may provide a set ofdifferent phase delays in each region of the LCOS optical element.

As further shown in FIG. 2, and by diagram 210, a fifth DOE may be asub-wavelength periodic binary grating. For example, the fifth DOE mayinclude a binary (two-level) structure with differing fill factors forstacks 212 or gaps 214 of the fifth DOE. Based on using a two-levelgrating structure for stacks 212 or gaps 214, the fifth DOE may beassociated with reduced manufacturing time and/or cost, improveddiffractive efficiency, and/or improved transmittance relative to thefirst DOE, the second DOE, the third DOE, and/or the fourth DOE. In someimplementations, a carrier period (also termed a pitch), dc, with regardto an x direction and a y direction, may be less than a wavelength ofincident light, and may be termed sub-wavelength. In this case, based onthe carrier period being sub-wavelength, a local effective refractiveindex, n_(eff), is caused for incident light.

In some implementations, a value for the local refractive index isvaried across a total period, d, of the fifth DOE. For example, based ona variable fill factor across a total period (e.g., a first carrierperiod, of the total period, having a first fill factor and a secondcarrier period, of the total period, having a second fill factor), thelocal effective refractive index may be varied across the total period.A fill factor may represent a ratio of a width, w, of a stack 212relative to a width of a carrier period in which the stack 212 islocated. Similarly, the fill factor may be related to a ratio of a widthof a space between a set of stacks 212, which may be termed a gap 214,relative to the width of the carrier period in which the gap 214 islocated. Based on varying the fill factor across the total period, thefifth DOE may be associated with a varying local effective refractiveindex across the total period, and may form a two-level DOE structure,also termed a binary DOE structure, which may be index matched to anenvironment or to a substrate over a range of fill factors of a carrierperiod. In some implementations, another type of multi-level DOEstructure may be formed using a carrier grating, such as a three-levelDOE, a four-level DOE, or another type of n-level DOE (n≥2). In someimplementations, a total period of a DOE may be varied with regard tomultiple axes (e.g., with regard to an x direction and a y direction).For example, a two dimensionally varying DOE may be used for adiffractive lens or another use case.

As indicated above, FIG. 2 is provided merely as an example. Otherexamples are possible and may differ from what was described with regardto FIG. 2.

FIGS. 3A-3G are diagrams of example implementations of DOEs. FIG. 3Ashows a cross-sectional view of an example DOE 300.

As shown in FIG. 3A, DOE 300 may include a substrate 302. In someimplementations, substrate 302 may be a glass substrate, a fused silicasubstrate, a borosilicate glass substrate, and/or the like. For example,substrate 302 may be a fused silica substrate with a thickness in arange from approximately 200 micrometers to approximate 3 millimeters,or of approximately 725 micrometers, and with a refractive index,n_(sub), of approximately 1.45. In some implementations, substrate 302may be associated with a total period, d, and each period may bedefined, with respect to a particular dimension of substrate 302 by aset of carrier periods, dc. For example, substrate 302 may include,extending planar with a top surface of substrate 302, a first carrierperiod from 0 dc to 1 dc, a second carrier period from 1 dc to 2 dc, athird carrier period from 2 dc to 3 dc, and a fourth carrier period from3 dc to 4 dc. In some implementations, each carrier period may beassociated with at least one stack, and may be a sub-wavelength period.For example, the first carrier period may include stack 304-1, thesecond carrier period may include stack 304-2, the third carrier periodmay include stack 304-3, and the fourth carrier period may include stack304-4. Similarly, each carrier period may be associated with at leastone gap. For example, the fourth carrier period may be associated with aportion of gap 306-1 (another portion of gap 306-1 may be included inthe third carrier period) and a portion of gap 306-2 (another portion ofgap 306-2 may be included in another carrier period of another totalperiod of DOE 300 on substrate 302). In this case, stacks 304 and gaps306 are castellated in a single dimension planar to a surface ofsubstrate 302.

In some implementations, each stack 304 may be associated with aparticular height, h, above a surface of each gap 306 and/or above asurface of substrate 302. For example, each stack 304 may be associatedwith a height in a range from approximately 0.5 micrometers toapproximately 6 micrometers (e.g., a 4 π period at 940 nanometers usingsilicon and a 2 π period at 1550 nanometers using fused silica), or ofapproximately 1.2 micrometers (e.g., a 4 π period at 1550 nanometersusing silicon). In some implementations, a first stack 304 may beassociated with a different height than a second stack 304. For example,stacks 304 of a common carrier period, of different carrier periods,and/or the like may be associated with different heights above a topsurface of substrate 302. In some implementations, each gap 306 may beassociated with a common depth from a top surface of stacks 304.Additionally, or alternatively, a first gap 306 may be associated with afirst depth from a surface of a stack 304 and a second gap 306 may beassociated with a second depth from a surface of a stack 304.Collectively, a stack 304 and a gap 306 may form a stack-and-gapstructure.

In some implementations, each carrier period may be associated with afill factor. The fill factor in one dimension and two dimensions,respectively may be calculated based on equations:

ff=w/dc  (1)

where ff represents the fill factor, w represents a width of a stack 304within a particular carrier period in one dimension or an area in twodimensions, and dc represents a width of the particular carrier periodin one dimension or an area in two dimensions. In some implementations,when a carrier period includes multiple stacks 304, w may represent asum of widths of the multiple stacks 304 in the carrier period, anaverage of widths of the multiple stacks 304 in the carrier period,and/or the like. In some implementations, the fill factor may vary withregard to carrier periods, of a total period, arranged along a dimensionplanar with a top surface of substrate 302, such that thinanti-reflection layers form stacks 304 and gaps 306 are index matched toan environment or to a substrate over a range of fill factors (e.g.,over the first through fourth fill factors as described below). Forexample, the first carrier period may be associated with a first fillfactor, the second carrier period may be associated with a second fillfactor, the third carrier period may be associated with a third fillfactor, and the fourth carrier period may be associated with a fourthfill factor.

In some implementations, each carrier period of a total period may beassociated with a different fill factor. In some implementations, two ormore carrier periods of the total period may be associated with a commonfill factor and another two or more carrier periods of the total periodmay be associated with a different fill factor. In some implementations,each carrier period of multiple total periods may be associated with arange of different fill factors. In some implementations, at least onecarrier period of a first total period and at least one carrier periodof a second total period may be associated with a common fill factor. Insome implementations, multiple total periods may be associated with acommon average fill factor, a different average fill factor, and/or thelike. In some implementations, each carrier period may be associatedwith a common fill factor. For example, when DOE 300 includes carrierperiods defined across two dimensions planar with a top surface ofsubstrate 302 (e.g., and stacks extend in a third dimensionperpendicular to the top surface of substrate 302, as shown), carrierperiods linearly arranged with regard to a first of the two dimensionsmay be associated with a common fill factor and carrier periods linearlyarranged with regard to a second of the two dimensions may be associatedwith different fill factors.

As shown in FIG. 3B, in a top-down view, another example implementationof a DOE, DOE 320, may include total periods with carrier periodsarranged in two dimensions extending planar with a top surface of asubstrate 322. In this case, the stacks and gaps are castellated in twodimensions planar to a surface of DOE 320.

As further shown in FIG. 3B, DOE 320 may include, in a first dimension,x, at least one total period, d_(x), and a set of carrier periodsdc_(x). Similarly, in a second dimension, y, DOE 320 may include atleast one total period, d_(y), and a set of carrier periods, dc_(y). Inthis way, a carrier grating of DOE 320 (e.g., stacks and gaps of DOE320) may provide a two-dimensional polarization independent DOE. Forexample, DOE 320 includes carrier periods 324-1-1, 324-2-1, 324-3-1, and324-4-1 aligned linearly in the first dimension. Similarly, DOE 320includes carrier periods 324-1-1, 324-1-2, 324-1-3, and 324-1-4 alignedlinearly in the second dimension. In this case, carrier periods alignedin the second dimension are each associated with a common fill factor,and carrier periods aligned in the first dimension are each associatedwith a different fill factor. For example, stacks 326-1-1 and 326-1-2are associated with a common width, resulting in a common fill factor,and stacks 326-1-1 and 326-2-1 are associated with different widths,resulting in a range of different fill factors. In some implementations,a pattern or arrangement of stacks and gaps in the carrier period may beselected based on a particular design technique. For example, atwo-dimensional rigorous grating theory technique, a thin film theorytechnique, a simulated annealing and steepest descent technique, and/orthe like may be used to identify a pattern or arrangement of gaps andstacks to provide a particular phase delay at a particular wavelengthfor which stacks and gaps provide an anti-reflection functionality.

As shown in FIG. 3C, and by diagram 340, an example phase profile ofphase delays is provided for carrier periods of a DOE described herein,such as for DOE 300 and/or for DOE 320 with respect to the first (x)dimension. For example, for the first carrier period, a (relative) phasedelay of 0 is caused by at least one stack and/or at least one gap ofthe first carrier period. Similarly, for the second carrier period, aphase delay of π/2 is caused; for the third carrier period, a phasedelay of π is caused; and for the fourth carrier period, a phase delayof 3π/2 is caused.

In some implementations, the phase delay of a DOE described herein maybe configured for a particular spectral range. For example, the phasedelay may be configured for a spectral range at which the stacks andgaps provide an anti-reflection functionality, such as a spectral rangewith a center illumination wavelength of 1550 nanometers. In this case,a width of a grating formed by the stacks and gaps may be less than 1550nanometers.

Although described herein in terms of a particular set of phase delays,other phase delays are possible, such as other equally spaced phasedelays (e.g., 0, π/4, π/2, 3π/4, π), other non-equally spaced phasedelays (e.g., 0, π, 3π/2, 7π/8), a combination of equally spaced phasedelays and non-equally spaced phase delays, and/or the like.

As shown in FIG. 3D, another example implementation of a DOE, DOE 360,may include multiple thin layers (e.g., thin film layers). For example,stacks of DOE 360 may be manufactured from multiple layers of thin filmson a surface of substrate 362. In this case, a stack may include a firstlayer 364-1 of silicon, a second layer 364-2 of silicon dioxide, a thirdlayer 364-3 of silicon, a fourth layer 364-4 of silicon dioxide, and afifth layer 364-5 of silicon. In some implementations, layers 364-1 and364-2 may form an index-matched pair. Similarly, layers 364-4 and 364-5may form an index-matched pair. In contrast, layer 364-3 may be a spacerbetween the index-matched pairs that may be selected to control aneffective index of DOE 360.

In some implementations, layers 364 may be index-matched to substrate362, an air interface with layers 364, and/or the like. In this way,transmittance may be improved relative to other techniques for forming adiffractive optical element. Moreover, based on a diffractive index ofDOE 360 varying based on a fill factor of carrier periods of DOE 360,DOE 360 may be index-matched with reduced manufacturing difficultyrelative to index matching based only on material selection. In someimplementations, layers 364 may be deposited using a depositiontechnique. For example, layers 364 may be deposited using thin filmdeposition (e.g., sputter deposition and/or the like). In someimplementations, stacks may be formed from layers 364 using a maskingand etching technique.

In some implementations, layers 364-1 through 364-5 may be associatedwith a set of thicknesses. For example, DOE 360 may be associated with athickness of 53 nanometers for layer 364-1, 64 nanometers for layer364-2, 1000 nanometers for layer 364-3, 121 nanometers for layer 364-4,and 28 nanometers for layer 364-5. In this case, layer 364-3, which maybe a spacer layer between the index-matched pairs, provides a phasedelay that may be tuned by adjusting the fill factor of stacks and gapsformed using layers 364. In some implementations, layer 364-3 may beassociated with a refractive index satisfying a threshold, such as arefractive index greater than 2.0, a refractive index of approximately3.5, and/or the like. In some implementations, a spacer layer betweenindex-matched pairs, such as layer 364-3, may be omitted. For example,one or more index-matched pairs of thin film layers may be formed onsubstrate 362 consecutively and etched to form stacks without a spacerlayer, such as layer 364-3.

Although described herein in terms of a particular set of thicknesses,other thicknesses are possible to achieve an anti-reflectionfunctionality, a particular phase delay, a particular refractive index,and/or the like. In some implementations, layers 364 of a stack may beformed using a deposition procedure. For example, a silicon thin filmlayer, a silicon dioxide thin film layer, and/or the like may bedeposited onto a surface of substrate 362 to form a set ofanti-reflection layers that are configured as a set of stacks and a setof gaps. Additionally, or alternatively, the stacks and the gaps may beformed using an etching procedure. For example, after deposition ofsilicon, silicon dioxide, and/or the like to form thin film layers onsubstrate 362, the layers may be masked using a single masking step andetched using a single etching step to form gaps and stacks.

As shown in FIG. 3E, another example of a DOE 380 may include a variablefill factor and a three or more level relief pattern. For example,stacks of DOE 380 may include multiple layers of thin films on a surfaceof substrate 382 to form a multi-level DOE with varying fill factors. Inthis case, a stack may include a first layer 384-1 of silicon, a secondlayer 384-2 of silicon dioxide, a third layer 384-3 of silicon, a fourthlayer 384-4 of silicon dioxide, and a fifth layer 384-5 of silicon, asixth layer 384-6 of silicon dioxide, a seventh layer 384-7 of silicon,and an eighth layer 384-8 of silicon dioxide. In some implementations,layers 384-1 and 384-2 may form a first index-matched pair, layers 384-4and 384-5 may form a second index-matched pair, and layers 384-7 and384-8 may form a third index-matched pair. Further, layers 384-1 and384-2 may be a first anti-reflection structure 386-1, layers 384-4 and384-5 may form a second anti-reflection structure 386-2, and layers384-7 and 384-8 may form a third anti-reflection structure 386-3. Incontrast, layers 384-3 and 384-6 may be spacers between index-matchedpairs that may be selected to control an effective refractive index ofDOE 380.

In another example, a metal layer may be used as a layer of DOE 380. Forexample, rather than forming layers 384-1 and 384-2 onto a top surfaceof substrate 382, a metal layer may be used to replace anti-reflectionstructure 386-1 and substrate 382, and layer 384-3 may be formed onto atop surface of the metal layer.

In DOE 380, each carrier period includes multiple stacks and multiplegaps to configure a fill factor of each carrier period. For example, afirst carrier period from 0 dc to 1 dc includes a first stack with afirst height (e.g., layers 384-1 to 384-5) and width and a second stackwith a second height (e.g., layers 384-1 to 384-8) and width to form afirst fill factor ff₁. In contrast, a second carrier period from 1 dc to2 dc includes a third stack with the first height (e.g., layers 384-1 to384-5) and another width and a fourth stack with the second height(e.g., layers 384-1 to 384-8) and another width to form a second fillfactor ff₂. In this case, each of the first to fourth stacks isassociated with a different width to form the first fill factor and thesecond fill factor.

In another example, a carrier period may include multiple gapsassociated with different depths from a top surface of a thin film layertowards a top surface of a substrate. In some implementations, DOE 380may be formed onto a wafer, such as a vertical-cavity surface-emittinglaser (VCSEL). For example, DOE 380 may be formed onto a wafer includingone or more emitters oriented to emit through substrate 382 and towardthe top surface of substrate 382. Additionally, or alternatively, DOE380 may be formed onto a wafer including another optical element, suchas a vertical emitter array, a sensor, a sensor array, and/or the like.

As shown in FIG. 3F, another example implementation of an opticalelement 390 may include a substrate 392 with a first DOE 394-1 on afirst, top surface of substrate 392 and a second DOE 394-2 on a second,bottom surface of substrate 392. For example, thin film layers may bedeposited and/or formed on the top surface and the bottom surface ofsubstrate 392 to form a set of DOEs 394. In this way, a difficulty inaligning multiple DOEs may be reduced relative to mounting multiple DOEson multiple substrates and aligning the multiple substrates. In someimplementations, corresponding carrier periods of DOEs 394-1 and 394-2may be associated with common fill factors. For example, both DOE 394-1and DOE 394-2 may be associated with a first fill factor, ff₁, for afirst carrier period from 0 dc to 1 dc, and may be associated with asecond fill factor, ff₂, for a second carrier period from 1 dc to 2 dc.Additionally, or alternatively, corresponding carrier periods of DOEs394-1 and 394-2 may be associated with different fill factors.

As shown in FIG. 3G, another example implementation of an opticalelement 395 may include a substrate 396 with a DOE 397 and a fillmaterial 398. In this case, fill material 398 may be disposed into gapsbetween stacks and/or onto a surface of the stacks and/or substrate 396to create a planar surface for optical element 395. In this way, fillmaterial 398 may seal optical element 395 to prevent degradation ofoptical performance resulting from a presence of water, humidity, and/orthe like. In some implementations, fill material 398 may be associatedwith a particular refractive index matched to the stacks, such as arefractive index of approximately 1.6 to create a 1.9 differential withstacks with a refractive index of approximately 3.5. In this way, aphase delay is maintained when optical element 395 is in contact with,for example, water.

Although described herein in terms of a set of 5 layers, 8 layers,and/or the like, other quantities of layers are possible, such asadditional layers, fewer layers, or a different combination of layers.

As indicated above, FIGS. 3A-3G are provided merely as examples. Otherexamples are possible and may differ from what was described with regardto FIGS. 3A-3G.

FIGS. 4A-4D are diagrams 400-460 of example characteristics of a DOE.

As shown in FIG. 4A, diagram 400 shows a maximum available phase delayas a function of a grating thickness (e.g., a height of a stack or adepth of gap). In some implementations, a 4π maximum phase delay may beselected for a DOE based on manufacturability criterion. Some opticalsystems may require a threshold experienced phase delay between regionsof a DOE (e.g., between carrier periods), which may be configured basedon a fill factor of a DOE, of 0 to 2π. Deep reactive ion etching (DRIE)techniques may be used for an aspect ratio, which may be defined as aratio of a depth to a minimum feature size, of greater than 10 anddeep-ultra-violet (DUV) stepper and scanner techniques can be used toachieve features of greater than 100 nanometers. Thus, a gratingthickness of approximately 1 micrometer for the stacks may be achievedusing DRIE techniques and DUV stepper and scanner techniques, in someimplementations. In this case, a DOE may be configured with a 4π maximumphase delay (for a fill factor of 100% relative to a fill factor of 0%),which may enable the DOE to achieve a 2π maximum phase delay (for a fillfactor of 75% relative to a fill factor of 25%) using a 1 micrometeretch.

As further shown in FIG. 4A, and by diagram 400, a DOE may bemanufactured using silicon (Si) with a refractive index of 3.5, asilicon-nitrogen material (Si_(x)N_(y)) (e.g. silicon nitride) with arefractive index of 2.0, a silicon dioxide (SiO₂) material with arefractive index of 1.5, and/or the like. As shown in diagram 400,silicon may be selected as a material for etching to manufacture stacksof a DOE. In this case, silicon may enable a reduced thin layer (e.g.,thin film) thickness relative to other materials, thereby improvingmanufacturability. For example, for silicon dioxide, a thin film layerthickness of 4 micrometers, which may correspond to an aspect ratio of40, may be required to achieve a maximum phase delay of 720 degrees(4π). For silicon nitride, a thin film layer thickness of 2 micrometers,which may correspond to an aspect ratio of 20, may be required toachieve a maximum phase delay of 720 degrees. For silicon, a thin filmlayer thickness of 0.7 micrometers, which may correspond to an aspectratio of 7, may be required to achieve a maximum phase delay of 720degrees. In this way, selection of silicon for thin film layers reducesa maximum required thin film layer thickness and an aspect ratiorelative to other materials, thereby enabling improved manufacturabilityfor the DOE. In some implementations, silicon and silicon dioxide may beselected as thin film layers for the DOE, and a thin film layer may actas an integrated etch stop for etching the DOE to form a multi-levelrelief profile for stacks of the DOE. In some implementations, a fillmaterial may be deposited onto the thin layers after etching to fillgaps between etched stacks, thereby providing an index-matched materialfor the thin film layers to avoid degradation to phase delay performancerelating to a non-index-matched material coming in contact with theetched stacks, such as water.

As shown in FIG. 4B, and by diagram 420, a transmittance and areflectance may be determined for a DOE based on a fill factor of theDOE. In this case, the DOE may be a non-index-matched two-dimensionalsub-wavelength periodic carrier grating with a silicon thin film stack.As shown in diagram 420, for the non-index-matched DOE, transmittancemay be less than a threshold, such as less than 50%, less than 60%, lessthan 70%, less than 80%, less than 90%, less than 95%, less than 99%,and/or the like for differing grating fill factors. For example, averagetransmittance may be 83% across the fill factors. Similarly, reflectancemay be greater than a threshold, such as greater than 60%, greater than50%, greater than 40%, greater than 30%, greater than 20%, greater than10%, greater than 5%, greater than 1%, and/or the like.

As shown in FIG. 4C, and by diagram 440, a transmittance and areflectance may be determined for another DOE based on a fill factor ofthe other DOE. In this case, the other DOE is an index-matchedtwo-dimensional sub-wavelength periodic carrier grating with a siliconand silicon dioxide thin film layers forming stacks. As further shown indiagram 440 for the index-matched DOE, transmittance may be greater thana threshold, such as greater than 90%, greater than 95%, greater than99%, and/or the like for a range of fill factors from 0% to 100% and/ora subrange thereof. For example, average transmittance may be 97.4%across the range of fill factors. Similarly, reflectance may be lessthan a threshold, such as less than 10%, less than 5%, less than 1%,and/or the like for a range of fill factors from 0% to 100% and/or asubrange thereof. As a result, based on configuring a materialcomposition, a thickness, and a quantity of layers a transmissionefficiency of greater than 85%, greater than 95%, greater than 99%,and/or the like may be achieved over a range of fill factors. In thisway, index matching thin film layers of a DOE may result in improvedtransmittance and reduced reflectance, thereby improving opticalperformance relative to other techniques for manufacturing a DOE.

As shown in FIG. 4D, and by diagram 460, a phase delay may be determinedfor a DOE relative to a fill factor of carrier period of the DOE. Inthis case, the DOE may be an index-matched two-dimensionalsub-wavelength periodic carrier grating with a silicon and silicondioxide thin layers forming stacks. For example, for a fill factor ofbetween 35% and 65%, a 2π phase delay may be achieved with a DOEconfigured for a 4π maximum phase delay.

As indicated above, FIGS. 4A-4D are provided merely as examples. Otherexamples are possible and may differ from what was described with regardto FIGS. 4A-4D.

In this way, a carrier grating may provide a sub-wavelength periodstack-and-gap structured layers providing transmissive phase delay at awavelength, such that the sub-wavelength period stack-and-gap structuredlayers include a set of thin anti-reflection layers that are indexmatched to an environment or a substrate over a range of fill factors ofthe sub-wavelength period.

The foregoing disclosure provides illustration and description, but isnot intended to be exhaustive or to limit the implementations to theprecise form disclosed. Modifications and variations are possible inlight of the above disclosure or may be acquired from practice of theimplementations.

Some implementations are described herein in connection with thresholds.As used herein, satisfying a threshold may refer to a value beinggreater than the threshold, more than the threshold, higher than thethreshold, greater than or equal to the threshold, less than thethreshold, fewer than the threshold, lower than the threshold, less thanor equal to the threshold, equal to the threshold, or the like.

Even though particular combinations of features are recited in theclaims and/or disclosed in the specification, these combinations are notintended to limit the disclosure of possible implementations. In fact,many of these features may be combined in ways not specifically recitedin the claims and/or disclosed in the specification. Although eachdependent claim listed below may directly depend on only one claim, thedisclosure of possible implementations includes each dependent claim incombination with every other claim in the claim set.

No element, act, or instruction used herein should be construed ascritical or essential unless explicitly described as such. Also, as usedherein, the articles “a” and “an” are intended to include one or moreitems, and may be used interchangeably with “one or more.” Furthermore,as used herein, the term “set” is intended to include one or more items(e.g., related items, unrelated items, a combination of related andunrelated items, etc.), and may be used interchangeably with “one ormore.” Where only one item is intended, the term “one” or similarlanguage is used. Also, as used herein, the terms “has,” “have,”“having,” or the like are intended to be open-ended terms. Further, thephrase “based on” is intended to mean “based, at least in part, on”unless explicitly stated otherwise.

What is claimed is:
 1. A diffractive optical element, comprising:sub-wavelength period stack-and-gap structured layers providingtransmissive phase delay at a wavelength, wherein the sub-wavelengthperiod stack-and-gap structured layers include a set of thinanti-reflection layers that are index matched to an environment or asubstrate over a range of fill factors of the sub-wavelength period. 2.The diffractive optical element of claim 1, wherein the set of thinanti-reflection layers are index matched to the environment and to thesubstrate over the range of fill factors of the sub-wavelength period.3. The diffractive optical element of claim 1, wherein the set of thinanti-reflection layers include thin film layers.
 4. The diffractiveoptical element of claim 1, wherein the stack-and-gap structured layersare castellated in a single dimension planar to a top surface of thesubstrate.
 5. The diffractive optical element of claim 1, wherein thestack-and-gap structured layers are castellated in two dimensions planarto a top surface of the substrate.
 6. The diffractive optical element ofclaim 1, wherein the stack-and-gap structured layers include a spacerlayer; and wherein the transmissive phase delay corresponds to athickness of the spacer layer.
 7. The diffractive optical element ofclaim 6, wherein the spacer layer is a thin film layer.
 8. Thediffractive optical element of claim 1, wherein a transmissionefficiency of the diffractive optical element is greater than 85% overthe range of fill factors.
 9. The diffractive optical element of claim1, wherein a transmission efficiency of the diffractive optical elementis greater than 95% over the range of fill factors.
 10. The diffractiveoptical element of claim 1, wherein the stack-and-gap structured layersinclude at least one silicon layer and at least one silicon dioxidelayer.
 11. The diffractive optical element of claim 1, wherein thediffractive optical element is polarization independent at thewavelength.
 12. The diffractive optical element of claim 1, wherein amaximum transmissive phase delay between areas of the stack-and-gapstructured layers is greater than or equal to 2π.
 13. The diffractiveoptical element of claim 1, wherein a maximum transmissive phase delaybetween areas of the stack-and-gap structured layers is greater than orequal to 4π.
 14. The diffractive optical element of claim 1, wherein thestack-and-gap structured layers is disposed on a first surface of thesubstrate; and wherein other sub-wavelength period stack-and-gapstructured layers providing another transmissive phase delay at thewavelength is disposed on a second surface of the substrate, and whereinthe other sub-wavelength period stack-and-gap structured layers includeanother set of thin anti-reflection layers that are index matched to theenvironment or the substrate over the range of fill factors of thesub-wavelength period.
 15. The diffractive optical element of claim 1,wherein a fill material at least partially covers the stack-and-gapstructured layers.
 16. A diffractive optical element, comprising: astack of layers including a set of anti-reflection layers, wherein thestack of layers is transmissive for a wavelength, wherein a width of thestack of layers is divided into a set of periods, wherein a width ofeach period, of the set of periods, is shorter than the wavelength,wherein a period, of the set of periods, has a fill factor defining awidth of a gap in the period, wherein fill factors of different periodsare different, wherein a depth of the gap extends through the stack oflayers and through the set of anti-reflection layers, wherein eachperiod, of the set of periods, provides phase delay, at the wavelength,associated with a corresponding fill factor, and wherein, over a rangeof different fill factors, the set of anti-reflection layers is indexmatched to an environment in the gap or to a substrate.
 17. Thediffractive optical element of claim 16, wherein the set ofanti-reflection layers form at least two anti-reflection structures. 18.The diffractive optical element of claim 16, wherein the set ofanti-reflection layers form at least three anti-reflection structures.19. A diffractive optical element, comprising: stack-and-gap structuredlayers including at least one layer sandwiched between a first set ofanti-reflection layers and a second set of anti-reflection layers,wherein the stack-and-gap structured layers provide transmissive phasedelay at a wavelength, wherein the stack-and-gap structured layers havea period shorter than the wavelength, and wherein a materialcomposition, a thickness, and a quantity of layers of the first set ofanti-reflection layers and a material composition, a thickness, and aquantity of layers of the second set of anti-reflection layers areselected such that, at the wavelength, a greater than 85% transmissionefficiency is achieved over a range of fill factors of the period. 20.The diffractive optical element of claim 19, wherein the diffractiveoptical element is disposed on a first side of a substrate and anotherdiffractive optical element is disposed on a second side of thesubstrate.